Such deep trigonometric net is closely related to the deep kernel learning with the SM kernel [1]}. Now it becomes clear that the outer network represents the random function \(f_2\sim \mathcal {GP}(0,k_{\rm SM})\) . The hyper-data \({\bf Z, u}\)  constrain the inner function \(f_1\) , and in the limit when the hyper-data are dense the function \({\bf f}_1\)  becomes deterministic [2]}. Such situation is equivalent to passing the inputs to a parametric function and then to a GP. However, the probabilistic nature in \(f_1\)  in the sparse hyper-data limit is helpful for preventing overfitting in deep kernel learning with over-parameterized \( f_1\)  [3]}.
